Although those results could give me enough information to find a formula to find the T Total from the T Number, Now I will draw up some more T Shapes but this time all adjacent so that when I draw a table it will be easier to spot the relationship.

Note that 90 Degrees Rotations do not include ‘g’ the grid size so these formulae are independent of grid size.

I will now Rotate a T shape 180 Degrees about an external point using the vectors {2}

{-1}

123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081I have noticed that if u double the vector u reach the corresponding T Number straight away and if we use x and y instead of numbers we will now have 2*{ x }

{-yg}

So if we go 2x across from The T Number 30 we get to 34 and go down 2*yg

we take away two grid sizes which is equal to 18 which is also equal to going down 2 squares so we get the formula:

T=5N+7G+5(2x-2YG)

I will now apply a combined transformation so all I need to do is find the formula for the second transformation as I have the formula for a 180 degrees rotation about an external point: T=5N+7G+5(2A-2BG)

So If I Now translate by a vector {s}

{t} the formula will also include the translation {s}

{-gt} for each T Number , therefore the total; formula for the T-Total will be:

Related GCSE T-Total essays

So instead of adding (7g + 7) which in the 7 by 7 grid is equal to 56, to the previous "T"-total as I had done in the first rotation to get the next "T"-total for the first rotation, I subtracted (7g + 7)

works on all shapes as long as they are translated vertically or horizontally. The formula is '5n-70' So by substituting the values I get: 5x32 - 70 = 90 As you can see the formula works. I will now proceed unto rotation of the T-shapes in a 10x10 grid.

in pattern 6, the total of white squares which is 20 + the total of black squares which is 41 will gives us the total of squares in that pattern which is 61, even though this is plainly simple I have made a formula relating to this.

As you can see the numbers in the middle is going up in 5's because the grid width is 5. Here is the converted version so I can work out the formula for the T-Total. N N+5 N+9 N+10 N+11 T = (N)+(N+5)+(N+10)+(N+9)+(N+11)

30 87 31 92 32 97 From both these tables I can see a pattern and that is that the T -Total increases by 5 every time the T -Number increases. 37, 42, 47, 52, 82, 87, 92, 97 5 5 5 5 5 5 For this investigation I am